Flexibilize the definition of motion time spans

KomaMRIBase/src/KomaMRIBase.jl

@@ -53,7 +53,7 @@ export MotionList, NoMotion, Motion
 export Translate, TranslateX, TranslateY, TranslateZ
 export Rotate, RotateX, RotateY, RotateZ 
 export HeartBeat, Path, FlowPath
-export TimeRange, Periodic
+export TimeRange, Periodic, TimeCurve
 export SpinRange, AllSpins
 export get_spin_coords
 # Secondary

KomaMRIBase/src/motion/Interpolation.jl

@@ -0,0 +1,66 @@
+# We defined two types of Interpolation objects: Interpolator1D and Interpolator2D
+# 1D is for interpolating for 1 spin
+# 2D is for interpolating for 2 or more spins
+# This dispatch based on the number of spins wouldn't be necessary if it weren't for this:
+# https://github.com/JuliaMath/Interpolations.jl/issues/603
+# 
+# Once this issue is solved, this file should be simpler. 
+# We should then be able to define a single method for functions:
+#   - interpolate
+#   - resample
+# and delete the Interpolator1D and Interpolator2D definitions
+
+const Interpolator1D = Interpolations.GriddedInterpolation{
+    TCoefs,1,V,Itp,K
+} where {
+    TCoefs<:Real,
+    TNodes<:Real,
+    V<:AbstractArray{TCoefs},
+    Itp<:Interpolations.Gridded,
+    K<:Tuple{AbstractVector{TNodes}},
+}
+
+const Interpolator2D = Interpolations.GriddedInterpolation{
+    TCoefs,2,V,Itp,K
+} where {
+    TCoefs<:Real,
+    TNodes<:Real,
+    V<:AbstractArray{TCoefs},
+    Itp<:Interpolations.Gridded,
+    K<:Tuple{AbstractVector{TNodes}, AbstractVector{TNodes}},
+}
+function GriddedInterpolation(nodes, A, ITP)
+    return Interpolations.GriddedInterpolation{eltype(A), length(nodes), typeof(A), typeof(ITP), typeof(nodes)}(nodes, A, ITP)
+end
+
+function interpolate(d, ITPType, Ns::Val{1}, t)
+    _, Nt = size(d)
+    t_knots = _similar(t, Nt); copyto!(t_knots, collect(range(zero(eltype(t)), oneunit(eltype(t)), Nt)))
+    return GriddedInterpolation((t_knots, ), d[:], ITPType)
+end
+
+function interpolate(d, ITPType, Ns::Val, t)
+    Ns, Nt = size(d)
+    id_knots = _similar(t, Ns); copyto!(id_knots, collect(range(oneunit(eltype(t)), eltype(t)(Ns), Ns)))
+    t_knots  = _similar(t, Nt); copyto!(t_knots,  collect(range(zero(eltype(t)), oneunit(eltype(t)), Nt)))
+    return GriddedInterpolation((id_knots, t_knots), d, ITPType)
+end
+
+function resample(itp::Interpolator1D, t)
+    return itp.(t)
+end
+
+function resample(itp::Interpolator2D, t)
+    Ns = size(itp.coefs, 1)
+    id = _similar(t, Ns)
+    copyto!(id, collect(range(oneunit(eltype(t)), eltype(t)(Ns), Ns)))
+    return itp.(id, t)
+end
+
+function interpolate_times(t, t_unit, periodic, tq)
+    itp = GriddedInterpolation((t, ), t_unit, Gridded(Linear()))
+    return extrapolate(itp, periodic ? Interpolations.Periodic() : Flat()).(tq)
+end
+
+_similar(a, N) = similar(a, N)
+_similar(a::Real, N) = zeros(typeof(a), N)

KomaMRIBase/src/motion/Motion.jl

@@ -11,7 +11,7 @@ that are affected by that motion.
 
 # Arguments
 - `action`: (`::AbstractAction{T<:Real}`) action, such as [`Translate`](@ref) or [`Rotate`](@ref)
-- `time`: (`::AbstractTimeSpan{T<:Real}`, `=TimeRange(0.0)`) time information about the motion
+- `time`: (`::TimeCurve{T<:Real}`, `=TimeRange(0.0)`) time information about the motion
 - `spins`: (`::AbstractSpinSpan`, `=AllSpins()`) spin indexes affected by the motion
 
 # Returns
@@ -28,22 +28,22 @@ julia> motion =  Motion(
 """
 @with_kw mutable struct Motion{T<:Real}
     action::AbstractAction{T}
-    time  ::AbstractTimeSpan{T}   = TimeRange(zero(typeof(action).parameters[1]))
-    spins ::AbstractSpinSpan      = AllSpins()
+    time  ::TimeCurve{T}      = TimeRange(t_start=-oneunit(typeof(action).parameters[1]), t_end=zero(typeof(action).parameters[1]))
+    spins ::AbstractSpinSpan  = AllSpins()
 end
 
 # Main constructors
 function Motion(action) 
     T = first(typeof(action).parameters)
-    return Motion(action, TimeRange(zero(T)), AllSpins())
+    return Motion(action, TimeRange(t_start=-oneunit(T), t_end=zero(T)), AllSpins())
 end
-function Motion(action, time::AbstractTimeSpan)
+function Motion(action, time::TimeCurve)
     T = first(typeof(action).parameters)
     return Motion(action, time, AllSpins())
 end
 function Motion(action, spins::AbstractSpinSpan)
     T = first(typeof(action).parameters)
-    return Motion(action, TimeRange(zero(T)), spins)
+    return Motion(action, TimeRange(t_start=-oneunit(T), t_end=zero(T)), spins)
 end
 
 # Custom constructors
@@ -54,7 +54,7 @@ end
 - `dx`: (`::Real`, `[m]`) translation in x
 - `dy`: (`::Real`, `[m]`) translation in y 
 - `dz`: (`::Real`, `[m]`) translation in z
-- `time`: (`::AbstractTimeSpan{T<:Real}`) time information about the motion
+- `time`: (`::TimeCurve{T<:Real}`) time information about the motion
 - `spins`: (`::AbstractSpinSpan`) spin indexes affected by the motion
 
 # Returns
@@ -65,7 +65,7 @@ end
 julia> translate = Translate(0.01, 0.02, 0.03, TimeRange(0.0, 1.0), SpinRange(1:10))
 ```
 """
-function Translate(dx, dy, dz, time=TimeRange(zero(eltype(dx))), spins=AllSpins())
+function Translate(dx, dy, dz, time=TimeRange(t_start=-oneunit(eltype(dx)), t_end=zero(eltype(dx))), spins=AllSpins())
     return Motion(Translate(dx, dy, dz), time, spins)
 end
 
@@ -76,7 +76,7 @@ end
 - `pitch`: (`::Real`, `[º]`) rotation in x
 - `roll`: (`::Real`, `[º]`) rotation in y 
 - `yaw`: (`::Real`, `[º]`) rotation in z
-- `time`: (`::AbstractTimeSpan{T<:Real}`) time information about the motion
+- `time`: (`::TimeCurve{T<:Real}`) time information about the motion
 - `spins`: (`::AbstractSpinSpan`) spin indexes affected by the motion
 
 # Returns
@@ -87,7 +87,7 @@ end
 julia> rotate = Rotate(15.0, 0.0, 20.0, TimeRange(0.0, 1.0), SpinRange(1:10))
 ```
 """
-function Rotate(pitch, roll, yaw, time=TimeRange(zero(eltype(pitch))), spins=AllSpins())
+function Rotate(pitch, roll, yaw, time=TimeRange(t_start=-oneunit(eltype(pitch)), t_end=zero(eltype(pitch))), spins=AllSpins())
     return Motion(Rotate(pitch, roll, yaw), time, spins)
 end
 
@@ -98,7 +98,7 @@ end
 - `circumferential_strain`: (`::Real`) contraction parameter
 - `radial_strain`: (`::Real`) contraction parameter
 - `longitudinal_strain`: (`::Real`) contraction parameter
-- `time`: (`::AbstractTimeSpan{T<:Real}`) time information about the motion
+- `time`: (`::TimeCurve{T<:Real}`) time information about the motion
 - `spins`: (`::AbstractSpinSpan`) spin indexes affected by the motion
 
 # Returns
@@ -109,7 +109,7 @@ end
 julia> heartbeat = HeartBeat(-0.3, -0.2, 0.0, TimeRange(0.0, 1.0), SpinRange(1:10))
 ```
 """
-function HeartBeat(circumferential_strain, radial_strain, longitudinal_strain, time=TimeRange(zero(eltype(circumferential_strain))), spins=AllSpins())
+function HeartBeat(circumferential_strain, radial_strain, longitudinal_strain, time=TimeRange(t_start=-oneunit(eltype(circumferential_strain)), t_end=zero(eltype(circumferential_strain))), spins=AllSpins())
     return Motion(HeartBeat(circumferential_strain, radial_strain, longitudinal_strain), time, spins)
 end
 
@@ -120,7 +120,7 @@ end
 - `dx`: (`::AbstractArray{T<:Real}`, `[m]`) displacements in x
 - `dy`: (`::AbstractArray{T<:Real}`, `[m]`) displacements in y 
 - `dz`: (`::AbstractArray{T<:Real}`, `[m]`) displacements in z
-- `time`: (`::AbstractTimeSpan{T<:Real}`) time information about the motion
+- `time`: (`::TimeCurve{T<:Real}`) time information about the motion
 - `spins`: (`::AbstractSpinSpan`) spin indexes affected by the motion
 
 # Returns
@@ -137,7 +137,7 @@ julia> path = Path(
        )
 ```
 """
-function Path(dx, dy, dz, time=TimeRange(zero(eltype(dx))), spins=AllSpins())
+function Path(dx, dy, dz, time=TimeRange(t_start=-oneunit(eltype(dx)), t_end=zero(eltype(dx))), spins=AllSpins())
     return Motion(Path(dx, dy, dz), time, spins)
 end
 
@@ -149,7 +149,7 @@ end
 - `dy`: (`::AbstractArray{T<:Real}`, `[m]`) displacements in y 
 - `dz`: (`::AbstractArray{T<:Real}`, `[m]`) displacements in z
 - `spin_reset`: (`::AbstractArray{Bool}`) reset spin state flags
-- `time`: (`::AbstractTimeSpan{T<:Real}`) time information about the motion
+- `time`: (`::TimeCurve{T<:Real}`) time information about the motion
 - `spins`: (`::AbstractSpinSpan`) spin indexes affected by the motion
 
 # Returns
@@ -167,7 +167,7 @@ julia> flowpath = FlowPath(
        )
 ```
 """
-function FlowPath(dx, dy, dz, spin_reset, time=TimeRange(zero(eltype(dx))), spins=AllSpins())
+function FlowPath(dx, dy, dz, spin_reset, time=TimeRange(t_start=-oneunit(eltype(dx)), t_end=zero(eltype(dx))), spins=AllSpins())
     return Motion(FlowPath(dx, dy, dz, spin_reset), time, spins)
 end
 
@@ -192,7 +192,7 @@ function get_spin_coords(
     m::Motion{T}, x::AbstractVector{T}, y::AbstractVector{T}, z::AbstractVector{T}, t
 ) where {T<:Real}
     ux, uy, uz = x .* (0*t), y .* (0*t), z .* (0*t) # Buffers for displacements
-    t_unit = unit_time(t, m.time)
+    t_unit = unit_time(t, m.time.t, m.time.t_unit, m.time.periodic, m.time.duration)
     idx = get_indexing_range(m.spins)
     displacement_x!(@view(ux[idx, :]), m.action, @view(x[idx]), @view(y[idx]), @view(z[idx]), t_unit)
     displacement_y!(@view(uy[idx, :]), m.action, @view(x[idx]), @view(y[idx]), @view(z[idx]), t_unit)
@@ -201,7 +201,7 @@ function get_spin_coords(
 end
 
 # Auxiliary functions
-times(m::Motion) = times(m.time)
+times(m::Motion) = times(m.time.t, m.time.duration)
 is_composable(m::Motion) = is_composable(m.action)
 add_jump_times!(t, m::Motion) = add_jump_times!(t, m.action, m.time)
-add_jump_times!(t, ::AbstractAction, ::AbstractTimeSpan) = nothing
+add_jump_times!(t, ::AbstractAction, ::TimeCurve) = nothing

KomaMRIBase/src/motion/MotionList.jl

@@ -1,5 +1,6 @@
+include("Interpolation.jl")
 include("SpinSpan.jl")
-include("TimeSpan.jl")
+include("TimeCurve.jl")
 include("Action.jl")
 include("Motion.jl")
 
@@ -156,7 +157,7 @@ function get_spin_coords(
     ux, uy, uz = xt .* zero(T), yt .* zero(T), zt .* zero(T)
     # Composable motions: they need to be run sequentially. Note that they depend on xt, yt, and zt
     for m in Iterators.filter(is_composable, ml.motions)
-        t_unit = unit_time(t, m.time)
+        t_unit = unit_time(t, m.time.t, m.time.t_unit, m.time.periodic, m.time.duration)
         idx = get_indexing_range(m.spins)
         displacement_x!(@view(ux[idx, :]), m.action, @view(xt[idx, :]), @view(yt[idx, :]), @view(zt[idx, :]), t_unit)
         displacement_y!(@view(uy[idx, :]), m.action, @view(xt[idx, :]), @view(yt[idx, :]), @view(zt[idx, :]), t_unit)
@@ -166,7 +167,7 @@ function get_spin_coords(
     end
     # Additive motions: these motions can be run in parallel
     for m in Iterators.filter(!is_composable, ml.motions)
-        t_unit = unit_time(t, m.time)
+        t_unit = unit_time(t, m.time.t, m.time.t_unit, m.time.periodic, m.time.duration)
         idx = get_indexing_range(m.spins)
         displacement_x!(@view(ux[idx, :]), m.action, @view(x[idx]), @view(y[idx]), @view(z[idx]), t_unit)
         displacement_y!(@view(uy[idx, :]), m.action, @view(x[idx]), @view(y[idx]), @view(z[idx]), t_unit)
@@ -199,7 +200,7 @@ If `motionset::MotionList`, this function sorts its motions.
 - `nothing`
 """
 function sort_motions!(m::MotionList)
-    sort!(m.motions; by=m -> times(m)[1])
+    sort!(m.motions; by=m -> m.time.t_start)
     return nothing
 end
 

KomaMRIBase/src/motion/TimeCurve.jl

@@ -0,0 +1,67 @@
+"""
+    timecurve = TimeCurve(t, t_unit, periodic, duration)
+
+TimeCurve struct. It is a specialized type that defines a time curve. 
+(...)
+
+# Arguments
+- `t`: (`::AbstractVector{<:Real}`, `[s]`) time vector
+- `t_unit`: (`::AbstractVector{<:Real}`) y vector, it needs to be scaled between 0 and 1
+- `periodic`: (`::Bool`, `=false`) indicates whether the time curve should be periodically repeated
+- `duration`: (`::Union{<:Real,AbstractVector{<:Real}}`, `=1.0`)
+
+# Returns
+- `timecurve`: (`::TimeCurve`) TimeCurve struct
+
+# Examples
+```julia-repl
+julia> timecurve = TimeCurve(t=[0.0, 0.1, 0.3, 0.4], t_unit=[0.0, 0.6, 0.2, 0.0], periodic=true)
+```
+"""
+@with_kw struct TimeCurve{T<:Real}
+    t::AbstractVector{T}
+    t_unit::AbstractVector{T}
+    periodic::Bool                       = false
+    duration::Union{T,AbstractVector{T}} = oneunit(eltype(t))
+    t_start::T                           = t[1]
+    t_end::T                             = t[end]
+    @assert check_unique(t) "Vector t=$(t) contains duplicate elements. Please ensure all elements in t are unique and try again"
+end
+
+check_unique(t) = true
+check_unique(t::Vector) = length(t) == length(unique(t))
+
+# Main Constructors
+TimeCurve(t, t_unit, periodic, duration) = TimeCurve(t=t, t_unit=t_unit, periodic=periodic, duration=duration)
+TimeCurve(t, t_unit) = TimeCurve(t=t, t_unit=t_unit)
+# Custom constructors
+# --- TimeRange
+TimeRange(t_start::T, t_end::T) where T = TimeCurve(t=[t_start, t_end], t_unit=[zero(T), oneunit(T)])
+TimeRange(; t_start=0.0, t_end=1.0)     = TimeRange(t_start, t_end)
+# --- Periodic
+Periodic(period::T, asymmetry::T) where T = TimeCurve(t=[zero(T), period*asymmetry, period], t_unit=[zero(T), oneunit(T), zero(T)])
+Periodic(; period=1.0, asymmetry=0.5)     = Periodic(period, asymmetry)
+
+""" Compare two TimeCurves """
+Base.:(==)(t1::TimeCurve, t2::TimeCurve) = reduce(&, [getfield(t1, field) == getfield(t2, field) for field in fieldnames(typeof(t1))])
+Base.:(≈)(t1::TimeCurve, t2::TimeCurve)  = reduce(&, [getfield(t1, field)  ≈ getfield(t2, field) for field in fieldnames(typeof(t1))])
+
+""" times """
+function times(t, dur::AbstractVector)
+    tr      = repeat(t, length(dur))
+    scale   = repeat(dur, inner=[length(t)])
+    offsets = repeat(vcat(0, cumsum(dur)[1:end-1]), inner=[length(t)])
+    tr     .= (tr .* scale) .+ offsets
+    return tr
+end
+function times(t, dur::Real)
+    return dur .* t
+end
+
+""" unit_time """
+function unit_time(tq, t, t_unit, periodic, dur::Real)
+    return interpolate_times(t .* dur, t_unit, periodic, tq)
+end
+function unit_time(tq, t, t_unit, periodic, dur)
+    return interpolate_times(times(t, dur), repeat(t_unit, length(dur)), periodic, tq)
+end